stat mech

Question 1

zeroth law

Answer 1

if A and B are in equilibrium and B is in equilbrium with c then A and C are in equilibrium

Question 2

first law

Answer 2

work is a state function - the work required to go between states is independent of path

Question 3

adiabatic expansion

Answer 3

no heat - pressure and volume change, temp doesn’t

Question 4

heat capacity

Answer 4

partial of heat with respect to Temp at constant V or P

Question 5

Ideal gas law using heat capacities

Answer 5

Cp-Cv = PV/T = Nkb

Question 6

second law

Answer 6

there cannot be complete conversion of heat to work

Question 7

draw a pv diagram

Answer 7

adiabatic and isotherm curve

Question 8

adiabatic curve solution

Answer 8

PV^gamma for gamm=5/3

Question 9

entropy equation

Answer 9

dQ = TdS
S= kb ln(omega)

Question 10

what equaitno is implied by the first law

Answer 10

dE = dQ+dW

Question 11

enthalpy

Answer 11

cp = dH/dT``

Question 12

Helmholtz free energy

Answer 12

F = E-TS

–isothermal transformations with no work

Question 13

Gibbs free energy

Answer 13

–isothermal transformation with constant external work

G = E-TS-W

Question 14

extensive, fundamental thermo equation

Answer 14

dE = TdS+Fdx+mudN

Question 15

maxwell relations

Answer 15

these follow from the commutative rule of derivatives and give relations between the partial derivates at a constant variable to another (based on fund..eq)

Question 16

How to find stable points

Answer 16

minimum of U or minimum of enthalpy (H= U-Fx) if there is an external force

Question 17

Third law

Answer 17

The entropy of all systems at absolute zero can be taken as the universal constant= zero

Question 18

Liouvilles theorem

Answer 18

phase space density behave like an incompressible fluid, {A,B} = -{B,A}

Question 19

microcanonical ensemble

Answer 19

mechanically and adiabatically isolated
macrostate M=(E,x)

omega = int(dE1*exp(S1(E1)-S2(E-E1)/kb)

Question 20

two-level system

Answer 20

H = eN, where N is number of excited impurities

Omega = N!/N1!/(N-N1)!

1/T = dS/dE at constant N , then solve for E

Question 21

energy of an ideal gas with f degrees of freedom

Answer 21

E = (f/2)*(NkT)

Question 22

canonical ensemble

Answer 22

temperature of the system is known 
- it has a resevoir from which to draw heat 
- no external work
- uses the partition function 
Z =sum_u exp(-BH(u))

Question 23

Gibbs canonical ensemble

Answer 23

Heat and work are allowed
no chemical work
Z = sum_(u,x) exp(BJ.x-BH(u))
G = -kbTln(Z)

Question 24

grand canonical ensemble

Answer 24

chemical work and heat
no mechanical work
Z = sum_(u) exp(BuN(u)-BH(u))

Question 25

Which two ensembles are identical in the thermodynamic limit

Answer 25

canonical and microcanonical

Question 26

explain phase transitions

Answer 26

exist only in the thermodynamic limit (N=>infinity)
critical points = correspond to singularities in free energy
first order are discontinuous - lines separating phases
second order are continous - like past the critical point for ice

Question 27

monte carlo simulations

Answer 27

better explanation

Question 28

brownian motion

Answer 28

188 in kardar field